Simplify the following expression and state the condition under which the simplification is valid: $r = \dfrac{k^2 + 17k + 72}{k^2 + 9k}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 + 17k + 72}{k^2 + 9k} = \dfrac{(k + 8)(k + 9)}{(k)(k + 9)} $ Notice that the term $(k + 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k + 9)$ gives: $r = \dfrac{k + 8}{k}$ Since we divided by $(k + 9)$, $k \neq -9$. $r = \dfrac{k + 8}{k}; \space k \neq -9$